To make the pastry: Put the flour, sugar and salt in a food processor and pulse briefly with the butter, to a breadcrumb stage, then add the egg and 1-2 tablespoons chilled water to bring it together into a dough. Alternatively, rub the butter in by hand, then stir in the egg and water. Form into ball, flatten, then wrap and chill for at least 30 minutes.
Next make the filling: Put the apples, 2 tablespoons of Calvados or brandy and the butter, sugar and lemon zest into a pan and place over a low heat and stir until the butter melts. Increase the heat and simmer the mixture for 15-20 minutes, stirring occasionally until the apples have softened to a pulp. Tip into a bowl and set aside to cool and prepare the tart case.
Lightly butter and flour an 8inch/20cm loose-bottomed flan tin. Flour your surface lightly and gently roll out the pastry to the thickness of a £1 coin. Lift into the tin and press gently into the bottom and sides, trim away the excess pastry. Prick the base evenly with a fork, line with parchment paper and lentils/rice/beans. Chill for 1 hour.
Bake the pastry case at 200C/180 Fan/Gas 6 until the sides are light golden. Remove the paper and beans, reduce the temperature to 160C/140 Fan/Gas 4 and cook so the base dries out. Remove and fill with the apple puree. Quarter, core and thinly slice the eating apples, arrange them starting from the outside to create concentric circles overlapping as you go. Bake for 20-25 minutes at 180C/160 Fan/Gas 4 until the apples are soft on top and just slightly coloured. Gently warm the jam (I usually thin this with a little Calvados or brandy) and brush the apples to make an attractive finish. Slice and serve with crème fraiche, ice cream or custard.
Pastry
Filling
Topping